In this talk, I will present recent results obtained with Gilles
Carron (Nantes Université) and Ilaria Mondello (Université
Paris-Est Créteil). We work in the setting of closed Riemannian
manifolds satisfying a so-called Kato bound, that is to say, the
negative part of the optimal lower bound on the Ricci curvature lies in
some suitable Kato class. I will explain how this
assumption provides good analytic and geometric control on the manifold,
and how this yields that a closed Riemannian
manifold satisfying a strong Kato bound with maximal first Betti number
is necessarily diffeomorphic to a torus: this extends a
result by Colding and Cheeger-Colding obtained in the context of a lower
bound on the Ricci curvature.
Meeting ID: 856 7181 3066
Passcode: 360540